Psychrometric ratio formula and units

[ypwtb]

What is the usual formula for the "psychrometric ratio"?

I find two versions in on-line documents:

http://www.geocities.com/drying_guru/chapter1fundamentals.pdf

r = h / (M_air k_y)

http://www.probec.org/fileuploads/fl120336971099294500CHAP12_Dryers.pdf

page 12-3: r = h_c /( k c_s)

The latter seems more usual to me, but the units for k seem to be
"mass / (area * time)".

But these units differ from what I find in Wikipedia here:

http://en.wikipedia.org/wiki/Mass_transfer_coefficient

What is the "correct" formula for "psychrometric ratio" and what are the units in its factors?

Thanks,
Yittri

 

[IRstuff]

If you're going to use Wikipedia, then use the right article:

http://en.wikipedia.org/wiki/Psychrometrics

TTFN

FAQ731-376

 

[ypwtb]

The formula in this article

http://en.wikipedia.org/wiki/Psychrometrics

is like the latter of the two in the OP.

And it also has k with units of "mass / (area * time)".

This document

http://engineer.msu.ac.th/CD_Conference/conference/IDS2002/PDF/0259.pdf

Gives the units of k_y as (kg /( m^2 s)).

The Wiki article on Mass_transfer_coefficient is pretty lean. It gives the units for k_c, not k_y. From what I read in an old chemical engineering reference book on "unit operations", 'c' is for concentration and 'y' is for mole-fraction.

Perhaps more pedantic units for k_y might be "mass / (area * time * mole_fraction)", where mole_fraction is a dimensionless ratio?

This page

http://www3.abe.iastate.edu/Ae573_ast475/Physical_Treatment-Theory.htm

defines k_y in terms of humidity ratio.

So it seems that pedantic units for k_y would include some dimensionless ratio, but they reduce to "mass / (area * time)".

The units for the first formula in the OP seem odd:

r = (Power / (area * temp) / ((mass/mole) * (mass / (area * time))

which seems to be, in metric units:
r= mole-m^2 / (kg s^2 K)

There seems to be some controversy about what label applies to which formula:

http://engineer.msu.ac.th/CD_Conference/conference/IDS2002/PDF/0259.pdf

"Keey (1992) takes great care to distinguish between the psychrometric coefficient ?, which relates overall heat and mass transfer and hence the adiabatic saturation and wet-bulb temperatures, and the psychrometric ratio ? as defined by Wilke and Wasan (1965)"

The Wikipedia statement suggests that a dimensionless number is in view there:

http://en.wikipedia.org/wiki/Psychrometrics

"The psychrometric ratio of air-water vapor mixtures is approximately unity"

That would seem to exclude the first version in the OP, with the weird units noted above.

So perhaps the formula here

http://en.wikipedia.org/wiki/Psychrometrics

is the most accepted one?

Thanks,
Yittri

 

[IRstuff]

Just because something has the same name as something else doesn't make them the same. You can't randomly find quantities that have similar names from different disciplines and assume that they're even related.

TTFN

FAQ731-376

 

[ypwtb]

Both true. I'm not sure how to use those observations to fortify a conclusion in this situation.

Which of the two formulae in the OP do you count as defining the psychrometric ratio? Why that one? Or do you use some other definition?

Thanks,
Yittri